The proposed research involves development of probabilistic models for exploring two key aspects of molecular evolution variation of evolutionary rates over time and the relationship between protein structure and protein evolution. Models for the evolution of evolutionary rates will be developed and these models will serve as the basis for statistical techniques to separate the variation of evolutionary rates that is lineage-specific from the variation that is gene-specific. Models for the evolution of evolutionary rates will result in improved methods for estimating evolutionary divergence times. Widely used methods for estimating divergence times from molecular sequence data make the dubious assumption that rates of evolution are constant over time. This weakness will be addressed with the proposed research. Statistical tools resulting from this work should shed light on the histories of viral epidemics. The other concentration of this research will be on the relationship between protein structure and protein evolution. The effect of the phenotype on the survival of the genotype is central to evolution. Ongoing studies to characterize the impact of structural environment on the pattern and rate of amino acid replacement will continue. Careful attention will be given to the evolution of sites in B-sheets. Improved models for the organization of protein structure along a protein sequence will be pursued. Instead of concentrating solely on the 20 amino acid types found in most genomes, models of amino acid replacement will be framed in terms of codons. Secondary structure prediction of proteins will also be a focus will be framed in terms of codons. Secondary structure prediction of proteins will also be a focus.